Psylocke swapping her British body for a Japanese one is an integral part of her character, they have to address it somehow. Maybe she already has the Japanese body and they show flashbacks to how she got it, or even dialogue could work.

I don't think it's integral to her character - it just adds unnecessary (and convoluted) backstory to a movie that will already have other characters that will need backstory and focus as well.

Either just make her fully British/Caucasian or make her Asian. I prefer her Asian since that's her most popular form.